I got to thinking about the shockwave that occurs upon firing and I'm under the impression that it's about 18,000 fps. So I measure the barrels on my 22 3/8" .204, 16" .223 AR15, and 20" on my .243. I subtracted a cartridge length from each, divided that length by the fps I get from those loads, and deterimined the amount of time each bullet is in the barrel. Then I divided that length by 18,000 fps to determine one trip in the barrel. When I divide the shockwave time into the time the bullet spends in the barrel, I came up the the amount of times it would go back and force until the bullet exited the muzzle and found the following:

22 3/8" .204 Ruger - 6.64 times

20" .243 Winchester - 5.46 times

16" .223 Remington AR15 - 7.2 times.

The 16" .223 has the shortest barrel as well as the lowest velocity but it would seem to me it would be the hardest of the 3 to find a suitable load where the shockwave is closer to the breech rather than nearer the muzzle, since it's making more trips back and forth. Does this sound reasonable?

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Of course, knowing the best times doesn't help much without knowing what times you're actually getting. One more reason I love QuickLoad.

BTW, I don't think you want to subtract a cartridge length from the barrel. The vibration doesn't stop at the bullet start point or tip or cartridge mouth, it goes end to end.

Note that, if you're numbers are correct, multiples at/near ".5" would be near optimal, the shockwave should be back near the breach in that time frame. Your calculations seem somewhat close in one respect, when I did the math (last year, my uncle made a FileMaker program to spit out the numbers), most of my barrel times predicted by QuickLoad were in the vicinity of the 6th and 7th nodes.

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The problem, as you so eloquently put it, is choice.
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Thanks Brian, I'm not sure how to determine that chart? I subtracted a cartridge length since I was measureing the distance only the bullet has to travel. I would think an odd number of passes would put the shockwave at the muzzle and an even number near the breech.

And I realize that the bullet to the muzzle time would actually be less than the overall exit velocity but I was just trying to use some known basic data and see how much I had to tweak the bullet speed to alter the number of shockwave passes.

After some testing all year, I've found some good loads for my .204 and .223. Now I might play with the OAL to see if I can improve those even more. Thanks.

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__________________
Still happily answering to the call-sign Peetza.
---
The problem, as you so eloquently put it, is choice.
-The Architect
-----
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.

This is not a simple division problem. The distance from bullet to breech is constantly increasing as the bullet travels down the barrel and the bullet is accelerating, so the change in distance the shock wave travels is not linear. This is a differential equations calculus problem.

Can the information you guys are discussing be put to simplest terms...?
IE....is there a "sweet spot " between a given barrel length and velocity nodes....?
would this be applicable to retrieve a powder for given bullet/caliber?

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Still happily answering to the call-sign Peetza.
---
The problem, as you so eloquently put it, is choice.
-The Architect
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He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.

This is beyond differential equations, it includes FEA as well. Barrel shape/contour, type of steel, and a bunch of other things.

Quote:

.is there a "sweet spot " between a given barrel length and velocity nodes....?

yes This is why barrel tuners work and why with every change of load your shot placement will differ, also why floating a barrel works.

In the late 1890's Schutzen shooters would often silver solder their barrels to the 1885 receiver to change the harmonics of the gun, not sure if they knew that is why the gun became more accurate or not though.

may i ask what kind of load(s) your using for your AR? bullets, powder charge etc.

My best load is 22.4 gr of 8208-XBR pushing a 60gr Nosler Vamnint tip with a cannelure and a light roll crimp after bullet seating with the Redding seater die. I was able to get a sub MOA at 100 yards with my Colt and I'm very happy with it - picture below.

I thought I'd try finding the perfect load for my ML this fall as well - it's good now, I'd like it to be great . . .

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The "vibrations" are, as Impalacustom suggests, complicated. The transverse whipping and the compressive shock wave discussed from the beginning are independent. Varmint Al's site has good FEA's of all the major modes of vibration except the compression wave, though he does mention in one of his pages that it exists. Nonetheless, his testing showed muzzle deflection imposed by high pressure gas deformation and recoil forces were dominant over the natural harmonic vibration modes. They occur after the "string is plucked" by firing and the bullet is gone. See the description and animated 3D FEA's here. Still, even the initial deflection comes out very close the 3rd harmonic timing when you run the numbers.

I've long suspected that "hummer" barrels may be those barrels for which the best tuned load has the transverse deflection and compression wave influences in sync. It may explain why the Houston Warehouse experiments found a particular barrel length tended to favor precision POI (21.75", IIRC, but I'd have to re-read the text to be sure my memory hadn't moved the number) regardless of chambering. I also suspect this may be why an adjustable tuner can make many kinds of ammo shoot very well, but still only make a few loads shoot bugholes. Those would, I suspect, be the ones were the vertical muzzle deflection, in particular, and the compression wave nulls would happen to coincide at the moment the bullet exits.

Two complications with Long's theory and calculator are barrel coupling to the receiver and the fact that the speed of sound in steel has a lot of dependency on grain orientation and alloy. He says that typically his calculator gets within 2% of sweet spot loads, so you still have a little tuning to do after you've loaded to the theoretically optimal barrel time. That degree of error could, indeed, be due to differences in the steel. In an email correspondence some years ago, Chris also told me that he had one barrel on a benchrest rifle he'd built that was the only one he'd tried for which the 2% error didn't work out, He believed that was because he had turned ultra high tolerance threads on the barrel that could not even be threaded hand tight. It took an action wrench just to get the barrel screwed down to the shoulder. He believed that in that case he had succeeded in coupling the receiver to the barrel so well that it became contiguous with the barrel as far as the reflecting compression wave was concerned, and its length had to be added to that of the barrel.

Fellas, that "shock" wave that travels back and forth in the barrel (at 15,000 to 18,000 fps depending on who's measuring it) causes smaller bore/groove diameter changes that what even the very best grade match barrels have when they're lapped to "perfection." Note that shock wave goes from the middle of the case in the chamber forward to the muzzle, then backwards to some point where it's reflected forward; that point may be the breech or back end of the receiver depending on how the barrel's fit to the receiver.

And the frequency that barrels whip at that causes the greatest muzzle axis angular movement is very low. The barrel doesn't even go through one complete whip cycle 1.1 millisecond after the primer detonates and the bullet leaves the muzzle. 1.1 milliseconds is what barrel time is for a whole bunch of rifle cartridges. And for handgun barrels, it's a whole lot shorter and if it's a revolver, how to you figure in the cylinder's effect?

Personally, I don't believe all this "shock wave" and "velocity timing" to get a given bullet to leave at some exact place in the muzzle's angle during barrel whip or diameter from shock wave expansion/contraction. Not when the same load's shot very accurate in all sorts of barrels; short skinny stiff ones as well as long thick whippy ones.

The barrel vibrations are a infinitesimal factor in the accuracy of a handgun. Virtually every other conceivable factor dwarfs the barrels vibrations into irrelevance.

VarmintAl has a very detailed analysis of barrel vibrations. He certainly doesn't conclude that there is no affect.

He specifically mentions 1.1milliseconds (.0011) as the time that the bullets would exit assuming constant acceleration and ignoring the time from primer ignition to bullet movement. (Neither of which matches real life)

His example, a 22" 416 stainless 30-06 barrel firing a 150gr GK bullet at approximately 3,300 fps says that the bullet exit time is .0025 seconds and almost exactly matches the barrels first upward swing.

Whether or not the receiver is counted as part of the length that the shockwave travels, something that would only happen with an EXTREMELY solid and tight barrel/receiver fit that you'd never see in a factory gun, the shockwave still has time to make at least 3 trips before the bullet exits.

__________________
Still happily answering to the call-sign Peetza.
---
The problem, as you so eloquently put it, is choice.
-The Architect
-----
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.

Brian, yes, 1.1's too low a number for barrel time examples; I overlooked that part of Al's site. And yes, most bullets exit someplace near the "hump' of the muzzle axis angular peak; some before and some after. The frequency of the barrel's whip cycle is pretty low compared to sound/shock speed in stainless steel.

Shock waves in stainless steel at 15000 fps travel 37.5 feet in .0025 seconds. In a 2-foot barrel, I think they'll make a lot more than 3 round trips.

But 3300 fps for a 150 grain bullet from a .30-06? That's a proof load plus!!!!

What's a link to Al's site on that barrel's info? Can't find one searching his web site.

The "3 trips" thing, VarmintAl said "4 or more" in regards to the barrel so I was using 3 as an example if the receiver is included, it would almost certainly be more.

I had a FileMaker based calculator my uncle made running at one point using Chris Long's equation. As I recall, most normal rifle barrel length are in the 6-7 region but that's going off memory. I'll have to ask him to put that program where I can get to it again so I can run the numbers.

Edit:

Got the program again, looks like my memory is faulty (again), here are the nodes around 25 milliseconds,

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